Einführung in die Komplexe Analysis

Elemente der Funktionentheorie
Author: Wolfgang Fischer,Ingo Lieb
Publisher: Springer-Verlag
ISBN: 3834893773
Category: Mathematics
Page: 214
View: 6028

Continue Reading →

In den Bachelor-Studiengängen der Mathematik steht für die Komplexe Analysis (Funktionentheorie) oft nur eine einsemestrige 2-stündige Vorlesung zur Verfügung. Dieses Buch eignet sich als Grundlage für eine solche Vorlesung im 2. Studienjahr. Mit einer guten thematischen Auswahl, vielen Beispielen und ausführlichen Erläuterungen gibt dieses Buch eine Darstellung der Komplexen Analysis, die genau die Grundlagen und den wesentlichen Kernbestand dieses Gebietes enthält. Das Buch bietet über diese Grundausbildung hinaus weiteres Lehrmaterial als Ergänzung, sodass es auch für eine 3- oder 4 –stündige Vorlesung geeignet ist. Je nach Hörerkreis kann der Stoff unterschiedlich erweitert werden. So wurden für den „Bachelor Lehramt“ die geometrischen Aspekte der Komplexen Analysis besonders herausgearbeitet.

Handbook of Complex Variables


Author: Steven G. Krantz,Steven George Krantz
Publisher: Springer Science & Business Media
ISBN: 9780817640118
Category: Mathematics
Page: 290
View: 847

Continue Reading →

A convenient reference for the scientist, student, or engineer whose work necessitates the use of the basic concepts in complex analysis, this is a book in which all the ideas and applications of complex analysis and differential equations are treated, as well as the applicable computational software.

Applied Complex Variables for Scientists and Engineers


Author: Yue Kuen Kwok
Publisher: Cambridge University Press
ISBN: 113948883X
Category: Mathematics
Page: N.A
View: 3678

Continue Reading →

This introduction to complex variable methods begins by carefully defining complex numbers and analytic functions, and proceeds to give accounts of complex integration, Taylor series, singularities, residues and mappings. Both algebraic and geometric tools are employed to provide the greatest understanding, with many diagrams illustrating the concepts introduced. The emphasis is laid on understanding the use of methods, rather than on rigorous proofs. Throughout the text, many of the important theoretical results in complex function theory are followed by relevant and vivid examples in physical sciences. This second edition now contains 350 stimulating exercises of high quality, with solutions given to many of them. Material has been updated and additional proofs on some of the important theorems in complex function theory are now included, e.g. the Weierstrass–Casorati theorem. The book is highly suitable for students wishing to learn the elements of complex analysis in an applied context.

Funktionentheorie


Author: Reinhold Remmert
Publisher: N.A
ISBN: 9783540553847
Category: Functions of complex variables
Page: 299
View: 7974

Continue Reading →

Diese dritte Auflage wurde zusammen mit dem zweitgenannten Autor kritisch durchgesehen, ergnzt und verbessert. Ein weiteres Kapitel ber geometrische Funktionentheorie und schlichte Funktionen enthlt einen Beweis der Bieberbachschen Vermutung. Der ... vorliegende zweite Band der Funktionentheorie erfllt voll die Erwartungen, die der erste Band geweckt hat. Wieder beeindrucken vor allem die hochinteressanten historischen Bemerkungen zu den einzelnen Themenkreisen, als besonderer Leckerbissen wird das Gutachten von Gau ber Riemanns Dissertation vorgestellt... Jedes einzelne Kapitel enthlt ausfhrliche Literaturangaben. Ferner werden oft sehr aufschlussreiche Hinweise auf die Funktionentheorie mehrerer Vernderlicher gegeben. Die vielen Beispiele und bungsaufgaben bilden eine wertvolle Ergnzung der brillant dargelegten Theorie. Der Rezensent bedauert, dass ihm nicht schon als Student ein derartig umfassendes, qualitativ hochstehendes Lehrbuch zur Verfgung stand." Monatshefte fr Mathematik

Handbook of Complex Analysis

Geometric Function Theory
Author: Reiner Kuhnau
Publisher: Elsevier
ISBN: 9780080495170
Category: Mathematics
Page: 876
View: 7105

Continue Reading →

Geometric Function Theory is that part of Complex Analysis which covers the theory of conformal and quasiconformal mappings. Beginning with the classical Riemann mapping theorem, there is a lot of existence theorems for canonical conformal mappings. On the other side there is an extensive theory of qualitative properties of conformal and quasiconformal mappings, concerning mainly a prior estimates, so called distortion theorems (including the Bieberbach conjecture with the proof of the Branges). Here a starting point was the classical Scharz lemma, and then Koebe's distortion theorem. There are several connections to mathematical physics, because of the relations to potential theory (in the plane). The Handbook of Geometric Function Theory contains also an article about constructive methods and further a Bibliography including applications eg: to electroxtatic problems, heat conduction, potential flows (in the plane). · A collection of independent survey articles in the field of GeometricFunction Theory · Existence theorems and qualitative properties of conformal and quasiconformal mappings · A bibliography, including many hints to applications in electrostatics, heat conduction, potential flows (in the plane).

Anschauliche Funktionentheorie


Author: Tristan Needham
Publisher: Oldenbourg Verlag
ISBN: 348670902X
Category: Mathematics
Page: 685
View: 2185

Continue Reading →

Needhams neuartiger Zugang zur Funktionentheorie wurde von der Fachpresse begeistert aufgenommen. Mit über 500 zum großen Teil perspektivischen Grafiken vermittelt er im wahrsten Sinne des Wortes eine Anschauung von der sonst oft als trocken empfundenen Funktionentheorie. "Anschauliche Funktionentheorie ist eine wahre Freude und ein Buch so recht nach meinem Herzen. Indem er ausschließlich seine neuartige geometrische Perspektive verwendet, enthüllt Tristan Needham viele überraschende und bisher weitgehend unbeachtete Facetten der Schönheit der Funktionentheorie." (Sir Roger Penrose)

Complex Variables for Scientists and Engineers

Second Edition
Author: John D. Paliouras,Douglas S. Meadows
Publisher: Courier Corporation
ISBN: 0486782220
Category: Mathematics
Page: 608
View: 9771

Continue Reading →

Outstanding undergraduate text provides a thorough understanding of fundamentals and creates the basis for higher-level courses. Numerous examples and extensive exercise sections of varying difficulty, plus answers to selected exercises. 1990 edition.

Control Theory, 2nd Edition


Author: J.R. Leigh
Publisher: IET
ISBN: 9780863413391
Category: Technology & Engineering
Page: 297
View: 1108

Continue Reading →

This fully revised and updated edition of "Control Theory" addresses recent developments in the field. It discusses how the rise of H∞ and similar approaches has allowed a combination of practicality, rigor and user interaction to be brought to bear on complex control problems and has helped bridge the gap between control theory and practice. The book also examines the effects of the rise of artificial intelligence techniques and the increasing availability of comprehensive software packages. The book concentrates on the structure, principles and context of control theory, and will be of interests to students and professionals alike.

Fourier Series and Boundary Value Problems


Author: James Ward Brown,Ruel Vance Churchill
Publisher: McGraw-Hill Science, Engineering & Mathematics
ISBN: N.A
Category: Boundary value problems
Page: 348
View: 6951

Continue Reading →

An introductory treatment of Fourier series and their applications to boundary value problems in partial equations that arise in engineering and physics. This revision incorporates up-to-date mathematics. Many sections have been rewritten to improve the motivation of the theory, and numerous illustrations and exercises have been added throughout the book.

Complex Variables and Their Applications


Author: Anthony D. Osborne
Publisher: Addison-Wesley
ISBN: N.A
Category: Mathematics
Page: 454
View: 3291

Continue Reading →

An understanding of functions of a complex variable, together with the importance of their applications, form an essential part of the study of mathematics. Complex Variables and their Applications assumes as little background knowledge of the reader as is practically possible, a sound knowledge of calculus and basic real analysis being the only essential pre-requisites. With an emphasis on clear and careful explanation, the book covers all the essential topics covered in a first course on Complex Variables, such as differentiation, integration and applications, Laurent series, residue theory and applications, and elementary conformal mappings. The reader is also introduced to the Schwarz-Christoffel transformation, Dirchlet problems, harmonic functions, analytic continuation, infinite products, asymptotic series and elliptic functions. Applications of complex variable theory to linear ordinary differential equations and integral transforms are also included. Complex Variables and their Applications is an ideal textbook and resource for second and final year students of mathematics, engineering and physics.

Partial Differential Equations and Boundary-value Problems with Applications


Author: Mark A. Pinsky
Publisher: McGraw-Hill Science, Engineering & Mathematics
ISBN: N.A
Category: Mathematics
Page: 526
View: 2283

Continue Reading →

Designed for the junior- and senior-level course in Partial Differential Equations, this new edition builds upon the solid strengths of the previous editions and has been revised to provide a more patient development of the core concepts. The material has been divided into three parts covering preliminary material, basic concepts, and advanced topics. Parts One and Two have also been reorganized and refined to provide more complete examples to help students master the content. The Sturm-Louiville Theory has been placed at the end of Chapter One and the coverage of infinite series and ordinary differential equations has been moved to an appendix.

Applied Complex Analysis with Partial Differential Equations


Author: Nakhlé H. Asmar,Gregory C. Jones
Publisher: N.A
ISBN: 9780130892393
Category: Mathematics
Page: 883
View: 7196

Continue Reading →

This reader-friendly book presents traditional material using a modern approach that invites the use of technology. Abundant exercises, examples, and graphics make it a comprehensive and visually appealing resource. Chapter topics include complex numbers and functions, analytic functions, complex integration, complex series, residues: applications and theory, conformal mapping, partial differential equations: methods and applications, transform methods, and partial differential equations in polar and spherical coordinates. For engineers and physicists in need of a quick reference tool.